Question: Simplify the following expression: $k = \dfrac{1}{10r} - \dfrac{1}{2r}$
Solution: In order to subtract expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $10r$ and $2r$ $\lcm(10r, 2r) = 10r$ $ k = \dfrac{1}{1} \cdot \dfrac{1}{10r} - \dfrac{5}{5} \cdot \dfrac{1}{2r} $ $k = \dfrac{1}{10r} - \dfrac{5}{10r}$ $k = \dfrac{1 -5}{10r}$ $k = \dfrac{-4}{10r}$ Simplify the expression by dividing the numerator and denominator by 2: $k = \dfrac{-2}{5r}$